It depends. You can gross up your SSI, and unless you are getting more income, maybe child support or something like that, you may have a lower price range, but still, you can buy a home.
There are city assistance programs that help with the down payment on simple interest, that you will not have to pay on until you sell or refinance. All cities have different programs so it depends where you are looking.
You may also qualify for CalStrs, about .5% down payment. Or if you have VA benefits, you don't have to put any money down. There is CALHFA which is little money down. Some properties require 3% down if they are HUD homes. It's a lot to chew. Maybe you can email me to be more specific about where you are looking to buy and I can give you a more direct answer.